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3

Even if it is not completely physical in some computational FV codes like OpenFOAM exist something called "inletOutlet" boundary condition that make the speed 0 at the boundary when it assumes negative values (or opposite to the sign of your outlet condition). You can find an explanation here and here. Even if it can be a solution, I suggest you to ...


4

Let's do it for the left boundary point $x=a$, and for simplicity assume $a=0$. To implement $u_x$=0 at $x$=0, assume the function $u(x)$ is even in the vicinity of $x$=0, and let the grid points be $x_0=0$, $x_1=h$, etc. Then, using the symmetry of the function, $u(-x_1)=u(x_1)$, the second derivative evaluated with the standard second-order accurate ...


10

I have found that I must keep the value of dt near dx or the results become unstable This behavior you have noticed is known as the Courant–Friedrichs–Lewy (CFL) condition. Indeed, there are timestep restrictions that are related to spatial refinement and choice of time integration method. Due to the diffusion term in 13a, the timestep must satisfy an ...


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